Question: Solve for $x$ and $y$ using elimination. ${3x+4y = 34}$ ${6x+3y = 63}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-2$ ${-6x-8y = -68}$ $6x+3y = 63$ Add the top and bottom equations together. $-5y = -5$ $\dfrac{-5y}{{-5}} = \dfrac{-5}{{-5}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {3x+4y = 34}\thinspace$ to find $x$ ${3x + 4}{(1)}{= 34}$ $3x+4 = 34$ $3x+4{-4} = 34{-4}$ $3x = 30$ $\dfrac{3x}{{3}} = \dfrac{30}{{3}}$ ${x = 10}$ You can also plug ${y = 1}$ into $\thinspace {6x+3y = 63}\thinspace$ and get the same answer for $x$ : ${6x + 3}{(1)}{= 63}$ ${x = 10}$